Suppose that Pepsi and Coke are competing in a horizon-
tally differentiated Bertrand market and setting prices.
The demand curves are as follows:
Qc = 40-5Pc + 4Pp
Qc = 100-2Pp + Pc
Coke face marginal cost MCc = 12 and Pepsi faces
marginal cost MCp = 8.
(a) Write the equation for the demand for coke in terms
of price Pc as a function of Pp and Qc.
(b) Determine the marginal revenue for Coke as a func-
tion of Pp and Qc.
(c) Find the equation that tells how much Coke would
produce for any price Pp using the above.
(d) Find the reaction function for Coke (Pc as a func-
tion of Pp ) using your answer above.
(e) Find the reaction function for Pepsi.
(f) Determine the Bertrand equilibrium.